问题 解答题
(1)
1
1×2
+
1
2×3
+
1
3×4
+…+
1
99×100
     
(2)6.8×
8
25
+0.32×4.2-8÷25

(3)
1
1×5
+
1
5×9
+
1
9×13
+…+
1
33
×
1
37
    
(4)1
1
4
-
9
20
+
11
30
-
13
42
+
15
56
答案

(1)

1
1×2
+
1
2×3
+
1
3×4
+…+
1
99×100

=(1-

1
2
)+(
1
2
-
1
3
)+(
1
4
-
1
5
)+(
1
5
-
1
6
)+…(
1
98
-
1
99
)+(
1
99
-
1
100
),

=1-

1
100

=

99
100
.     

(2)6.8×

8
25
+0.32×4.2-8÷25,

=6.8×

8
25
+
8
25
×4.2-
8
25

=

8
25
×(6.8+4.2-1),

=

8
25
×10,

=3.2.    

(3)

1
1×5
+
1
5×9
+
1
9×13
+…+
1
33
×
1
37

=

1
4
×(1-
1
5
)+
1
4
×(
1
5
-
1
9
)+
1
4
×(
1
9
-
1
13
)+…
1
4
×(
1
33
-
1
37
),

=

1
4
×(1-
1
5
+
1
5
-
1
9
+
1
9
-
1
13
+…+
1
33
-
1
37
),

=

1
4
×(1-
1
37
),

=

1
4
×
36
37

=

9
37
.   

(4)1

1
4
-
9
20
+
11
30
-
13
42
+
15
56

=1

1
4
-(
1
4
+
1
5
)+(
1
5
+
1
6
)-(
1
6
+
1
7
)+(
1
7
+
1
8
),

=1

1
4
-
1
4
-
1
5
+
1
5
+
1
6
-
1
6
-
1
7
+
1
7
+
1
8

=1+

1
8

=1

1
8

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